# PE 4 - Venn Diagram | LR - Venn Diagram

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**Answer the next 2 questions based on the information given below.**

Abdul, Mala and Chetan went bird watching. Each of them saw one bird that none of the others did. Each pair saw one bird that the third did not. And one bird was seen by all three. Of the birds Abdul saw, two were yellow. Of the birds Mala saw, three were yellow. Of the birds Chetan saw, four were yellow.

**PE 4 - Venn Diagram | LR - Venn Diagram**

How many yellow birds were seen in all?

Answer: 5

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**Explanation** :

Each of them alone saw 1 bird.

Each pair saw 1 bird which the third did not see.

All three of them saw 1 bird.

Chetan saw 4 yellow birds, hence all 4 birds that Chetan saw were yellow.

Abdul saw only 2 yellow birds while Mala saw 3 yellow birds. Hence, the third yellow bird which Mala saw was seen by Mala alone.

There are a total of 5 yellow birds.

Hence, 5.

Workspace:

**PE 4 - Venn Diagram | LR - Venn Diagram**

How many non-yellow birds were seen in all?

Answer: 2

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**Explanation** :

Consider the solution to first question of this set.

There are a total of 2 non-yellow birds.

Hence, 2.

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**Answer the next 5 questions based on the information given below.**

300 students of a school went for picnic. Each student brought certain amount of money with himself/herself. The amount they bring with them is an integral multiple of 20, 30 or 50.

A: Students whose amount is a multiple of 20.

B: Students whose amount is a multiple of 30.

C: Students whose amount is a multiple of 50.

- number of students who belong to only A is twice the number of students who belong to B and C.
- The number of students who belong to A, B and C is 8.
- The number of students who belong to B is same as the number of students who belong to C.
- The number of students who belong to A and B is 8 more than the number of students who belong to A and C.
- The number of students who belong to only A and C is 8 more than the number of students who belong to only A and 16 less than the number of students who belong to only B.

**PE 4 - Venn Diagram | LR - Venn Diagram**

How many students are in A but not B?

Answer: 88

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**Explanation** :

From (2): The number of students who belong to A, B and C is 8.

From (1): The number of students who belong to only A is twice the number of students who belong to B and C.

Let the number of students belonging to only B and C is x.

⇒ Number of students belonging to B and C = x + 8

∴ Number of students belonging to only A = 2x + 16

From (5): Number of students belonging to only A and C = (2x + 16) + 8 = 2x + 24

Also, number of students belonging to only B = (2x + 24) + 16 = 2x + 40

From (4): Number of students belonging to only A and B = Number of students belonging to only A and C + 8

⇒ Number of students belonging to only A and B = 2x + 24 + 8 = 2x + 32

[Since 8 is common to both regions mentioned in the point, we have ignored it.]

From (3): Number of students belonging to B = 8 + 2x + 32 + x + 2x + 40

Number of students belonging to C = 8 + x + 2x + 24 + only C

⇒ 8 + x + 2x + 24 + only C = 8 + 2x + 32 + x + 2x + 40

⇒ only C = 2x + 48

Now, total number of students is 300.

⇒ (2x + 16) + (2x + 32) + (2x + 40) + 8 + (2x + 24) + x + (2x + 48) = 300

⇒ 11x + 168 = 300

⇒ x = 12

∴ Number of students in A but not B = 2x + 16 + 2x + 24 = 4x + 40 = 88

Hence, 88.

Workspace:

**PE 4 - Venn Diagram | LR - Venn Diagram**

If no student brought more than Rs. 500 while 4 students brought Rs. 450, how many students brought Rs. 150?

Answer: 8

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**Explanation** :

Consider the solution to first question of this set.

Amounts of 150 and 450 are multiples of 30 and 50 but not 20. Hence, they belong to only B and C.

Since, maximum amount students brought is 500, hence the 8 students belonging to only B and C must have brought either Rs. 150 or Rs. 450.

If 4 students brought Rs. 450, hence 12 - 4 = 8 students brought Rs. 150.

Hence, 8.

Workspace:

**PE 4 - Venn Diagram | LR - Venn Diagram**

No student brought an amount between 170 and 260 and the highest amount that anyone brought is Rs. 300. What is the average amount with students who belong to C? [Round off your answer to the nearest integer.]

Answer: 90

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**Explanation** :

Consider the solution to first question of this set.

Now, since no student brought an amount between 170 and 260 and the highest amount that anyone brought is Rs. 300, we can have the following amounts (written in green) for each category in C.

∴ Average = (50 × 72 + 100 × 48 + 300 × 8 + 150 × 12) / (72 + 48 + 8 + 12) = 90.

Hence, 90.

Workspace:

**PE 4 - Venn Diagram | LR - Venn Diagram**

What is the minimum number of students who brought more than Rs. 100?

Answer: 20

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**Explanation** :

Consider the solution to first question of this set.

The diagram below shows the least amount (in green) in each category.

∴ Minimum students who brought more Rs. 100 = 8 + 12 = 20.

Hence, 20.

Workspace:

**PE 4 - Venn Diagram | LR - Venn Diagram**

If nobody brought an amount between Rs. 160 and 260 or more than Rs. 300 and the number of students who brought Rs. 50 was twice the number of students who brought 60, what is the average amount of the students who belong to more than one of A, B or C?

[Round off your answer to neared integer.]

Answer: 111

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**Explanation** :

Consider the solution to first question of this set.

Now, since no student brought an amount between 160 and 260 and the highest amount that anyone brought is Rs. 300, we can have the following amounts (written in green) for each category.

∴ Average = (100 × 48 + 150 × 12 + 300 × 8 + 60 × 32 + 120 × 24) / (48 + 8 + 12 + 56) = 111

Hence, 111.

Workspace:

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